The June 2015 progress report states that Snowblind engine games, such as Champions: Return to Arms, will now function in Hardware mode without the half-screen bug.
However, after downloading and installing r5875 (fresh install), the bug still persists.
Are there settings I can change to prevent the half-screen bug in Hardware mode as the progress report says?

Download the 4GB patch attached to Refraction's post here. Extract it somewhere, run it and apply it to pcsx2.exe.

Make sure you set your resolution in the GSDX settings to Native or to one of the 2x, 3x, 4x Native settings - if you use a custom resolution you'll still get the half-screen issue. Using 4x Native or higher can result in VRAM usage of over 4GB in some spots - wouldn't recommend it unless your graphics card has >6GB VRAM.